Assertion (A) is true: lyases (EC class 4) catalyze the cleavage of C-C, C-O, C-N, and other bonds by elimination, leaving double bonds or adding groups to double bonds. Reason (R) is true: hydrolases (EC class 3) catalyze hydrolysis, transferring functional groups to water as an acceptor. However, (R) describes hydrolases and is not an explanation for lyase mechanism.

Enzyme reaction pathway: Enzyme meets substrate (C) $\rightarrow$ Substrate binds to active site forming Enzyme-Substrate complex [ES] (A) $\rightarrow$ Catalytic conversion produces Enzyme-Product complex [EP] (B) $\rightarrow$ Product dissociates, regenerating free enzyme (D). Correct order: (C), (A), (B), (D).

Allopurinol is a purine analogue and suicide inhibitor of xanthine oxidase. It is metabolized by xanthine oxidase to alloxanthine (oxypurinol), which tightly binds the molybdenum active site, blocking uric acid synthesis to treat gout and hyperuricemia.

Allosteric control of bacterial aspartate transcarbamoylase (ATCase):

• Adenosine triphosphate (ATP) is a purine nucleotide that signals an abundance of purines and energy; it binds to the regulatory subunits of ATCase, stabilizing the high-affinity, catalytically active relaxed (R) state, thereby acting as a potent allosteric activator to coordinate balanced purine-to-pyrimidine pools.
• Cytidine triphosphate (CTP) is the end-product of pyrimidine synthesis that acts as a feedback allosteric inhibitor by stabilizing the low-affinity tense (T) state.
• Cytidine monophosphate (CMP) does not serve as the primary allosteric effector.
• Thiamine triphosphate (TTP) is a coenzyme form of vitamin B1 unrelated to ATCase regulation.